02 Activity 02_Predicate Logic, Exercises of Discrete Mathematics

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PREDICATE LOGIC

02 Activity 02

APRIL 12, 2022

BSCS201 || DISCRETE MATHEMATICS 1

Let P(x): 𝐀 2 2 =𝐀 Find the following then identify their truth values.

1. P (1) P(x): 𝐀 2 2 =𝐀 P(1): (1) 2 2 = P(1): 12 = P(1): 12 ≠ 1 If we substitute integer 1 into the value of x in 𝐀 2 2 ,^ we^ will^ get^ the^ result^ of 1 2.^ Thus,^ P(1):^ 𝐀^2 2 =𝐀^ is^ FALSE.
2. P (2) P(x): 𝐀 2 2 =𝐀 P(2): (2)^2 2 = P(2): 42 = P(2): 2= If we substitute integer 2 into the value of x in 𝐀 2 2 ,^ we^ will^ get^ the^ result^ of
3. Thus, P(2): 𝐀 2 2 =𝐀^ is^ TRUE.
4. ꓯ n, P(n) ꓯ n, P(n) can be denoted as “For all natural numbers n, n is P”. This statement is FALSE since from the solution in item#1, if x=1, it denies the equality of 𝐀 2 2 =𝐀.
5. ꓱ n, P(n) ꓱ n, P(n) can be denoted as “For some natural numbers n, n is P”. This statement is TRUE since the solution in item#2 proved that P(2): 𝐀 2 2 =𝐀^ is^ true^ and^ false^ in item#1.